Same disclaimer: Not a lawyer.
Though you say "Our management company sees themselves as representing both sides," I kind of doubt that. Though I'm a Realtor, I use some specialized agents to rent out a property I own. And they wouldn't considering themselves as "representing both sides." True, there's the standard language in the listing agreement, similar to yours, saying that if I sell (under certain conditions), I owe a 6% commission. The intent is that they'd act as a listing agent, not under dual agency.
In that case--and likely in your case (non-lawyer disclaimer), the commission would be split just as it would be in most sales. You'd owe the 6% to the listing agent. That agent, in turn, would share that commission with the agent representing the buyers.
Further--again, not a lawyer--you'd have no contractual agreement with your friend's (or buyer's) agent. You've never promised to pay him a dime. All you've probably done is promised to pay your management company a 6% commission. Whatever agreement your friend (or other buyer) might have with his agent is none of your concern. You've promised nothing to the other agent; you owe nothing to the other agent.
Finally, keep two things in mind: (1) All commissions are negotiable. Ask to have that 6% lowered, if you so choose. The management company may or may not agree. (2) Contracts are negotiable. My rental property is in Virginia (if that makes any difference) and we've modified that provision in the listing agreement in certain ways so that, under various conditions, if the property is sold we are not obligated to use the agents who handled the rental and we are not obligated to pay them. So: Don't accept (or agree to) a contract you're not happy with.
Hope that helps.